Complex dynamics in a nonlinear duopoly model with heuristic expectation formation and learning behavior

Abstract

We develop a nonlinear duopoly model in which the heuristic expectation formation and learning behavior of two boundedly rational firms may engender complex dynamics. Most importantly, we assume that the firms employ different forecasting models to predict the behavior of their opponent. Moreover, the firms learn by leaning more strongly on forecasting models that yield more precise predictions. An eight-dimensional nonlinear map drives the dynamics of our approach. We analytically derive the conditions under which its unique steady state is locally stable and numerically study its out-of-equilibrium behavior. In doing so, we detect multiple scenarios with coexisting attractors at which the firms’ behavior yields distinctively different market outcomes.